Self-organization and Intervention of Nonlinear Multi-agent Systems

Sammanfattning: This dissertation concerns the self-organization behaviors in different types of multi-agent systems, and possible ways to apply interventions on top ofthat to achieve certain goals. A bounded confidence opinion dynamics modelis considered for the first two papers. Theoretical analysis of the model isperformed and modifications of the model are given so that it will have better properties in some aspect. Leader-follower based models are studied in the third to fifth papers where various optimal control problems are considered. Different methods such as Pontryagin minimum principle and dynamic programming are used to solve those optimal control problem. For complex problems, one may only get approximate solutions or suboptimal solutions.In Paper A and Paper B, we consider the continuous-time Hegselmann-Krause (H-K) model and its variations and target the problem of reaching consensus. A sufficient condition on the initial opinion distribution is givento guarantee consensus for the original continuous-time H-K model. A modified model is provided and proven to be able to lead a larger range of initial opinions to synchronization. An H-K model with an exo-system is also studied where sufficient conditions on the exo-system are given for the purpose of consensus.In Paper C and Paper D, optimal control problems with leader-followerbased multi-agent systems are discussed. Analytic solutions are derived if the dynamics is linear by applying Pontryagin minimum principle. For generalnon-linear leader-follower interactions, we provide a method that use sstatistic moments of the follower crowd to approximate the optimal control.The dynamic programming approach is used and certain approximation ofthe Hamilton-Jacobi-Bellman equations is needed. The computational burdenis so heavy that model predictive control method is required in practical applications.In Paper E, we apply a similar method to the approach used in PaperD to target a pollutant elimination problem. It implies that we can use themethod to attack optimal control problem with partial differential equation constraints by discretization in space. The dimension of the discretization is not related to the computational complexity since only the statistic moments are needed.